Question: Express your answer as a mixed number simplified to lowest terms. $7\dfrac{1}{5}-4\dfrac{6}{9} = {?}$
Simplify each fraction. $= {7\dfrac{1}{5}} - {4\dfrac{2}{3}}$ Find a common denominator for the fractions: $= {7\dfrac{3}{15}}-{4\dfrac{10}{15}}$ Convert ${7\dfrac{3}{15}}$ to ${6 + \dfrac{15}{15} + \dfrac{3}{15}}$ So the problem becomes: ${6\dfrac{18}{15}}-{4\dfrac{10}{15}}$ Separate the whole numbers from the fractional parts: $= {6} + {\dfrac{18}{15}} - {4} - {\dfrac{10}{15}}$ Bring the whole numbers together and the fractions together: $= {6} - {4} + {\dfrac{18}{15}} - {\dfrac{10}{15}}$ Subtract the whole numbers: $=2 + {\dfrac{18}{15}} - {\dfrac{10}{15}}$ Subtract the fractions: $= 2+\dfrac{8}{15}$ Combine the whole and fractional parts into a mixed number: $= 2\dfrac{8}{15}$